Persistent Heat Signature for Pose-oblivious Matching of Incomplete Models Tamal K. Dey, Kuiyu Li, Chuanjiang Luo, Pawas Ranjan, Issam Safa, Yusu Wang [The Ohio State University] (SGP 2010)

Problem Query and match partial, incomplete and pose-altered models

Previous Work [CTS03]; [OBBG09]; [KFR04]; [BCG08]; [L06]; [RSWN09] … No unified approach for pose-invariant matching of partial, incomplete models

Descriptor based Matching Represent shape with descriptor ‒ Compare descriptors Local vs Global descriptors Need a multi-scale descriptor to capture both local and global features

HKS [Sun-Ovsjanikov-Guibas 09]  Signifies the amount of heat left at a point x M at time t, if unit heat were placed at x when t=0 ‒ Isometry invariant ‒ Stable against noise, small topological changes ‒ Local changes at small t for incomplete models

HKS as Shape Descriptor Possible solutions: ‒ Choose the maxima values for some t Too many for small t Sensitive to incompleteness of shape for large t Need to choose a concise subset of HKS values

Persistent HKS

Persistence [Edelsbrunner et al 02] Tracks topological changes in sub-level sets Pairs point that created a component with one that destroyed it

Persistent Maxima with Region Merging Apply Persistence to HKS ‒ To obtain persistent maxima Region-merging algorithm

Persistent Maxima with Region Merging

Persistent Maxima

Feature Vector Assign a multi-scale feature vector to each persistent maximum ‒ HKS function values at multiple time scales A shape is represented by 15 feature vectors in 15D space

The Algorithm Compute the HKS function on input mesh for small t Find persistent maxima Compute HKS values for multiple t at the persistent maxima

Scalability Expensive to compute the eigenvalues and eigenvectors for large matrices Use an HKS-aware sub-sampling method

Scoring & Matching Pre-compute feature vectors for database Given a query ‒ Compute feature vectors of query ‒ Compare with feature vectors in database Score is based on L1-norm of feature vectors

Results 300 Database Models (22 Classes) ‒ 198 Complete ‒ 102 Incomplete 50 Query Models ‒ 18 Complete ‒ 32 Incomplete

Results

Comparison Eigen-Value Descriptor [JZ07] Light Field Distribution [CTSO03] Top-k Hit Rate ‒ Query hit if model of same class present in top-k results returned

Comparison

Conclusion Combine techniques from spectral theory and computational topology ‒ Fast database-style shape retrieval ‒ Unified method for pose-oblivious, incomplete shape matching Handling non-manifold meshes Matching feature-less shapes